Question: One more than the reciprocal of a particular number is $\frac{7}{3}$. What is the original number expressed as a common fraction?
Answer: Letting the original number be $x$, we must have $$1+\frac{1}{x}=\frac{7}{3}.$$ Subtracting 1 from both sides gives $$\dfrac{1}{x} = \dfrac{4}{3}.$$ Taking the reciprocal of both sides gives  $x=\boxed{\frac{3}{4}}.$